Many-to-Many Disjoint Path Covers in Two-Dimensional Bipartite Tori with a Single Vertex Fault
نویسندگان
چکیده
A paired many-to-many -disjoint path cover (-DPC for short) of a graph is a set of disjoint paths joining distinct source-sink pairs in which each vertex of the graph is covered by a path. A two-dimensional × torus is a graph defined as the product of two cycles and of length and , respectively. In this paper, we deal with an × bipartite torus, even ≥ , with a single faulty vertex, and present a necessary and sufficient condition for the torus to have a paired many-to-many 2-DPC connecting given two source-sink pairs as follows: Out of the four sources and sinks, exactly one of them has the same color as the faulty vertex.
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